Question $1(5\%)$

Suppose the scores for a certain exam are normally distributed with a mean of $70$ and a standard deviation of $3\mathrm{.}5.$ Find the z$-$score for an exam score of $77.$

Question $2(5\%)$

Suppose that the minimum and maximum values for test scores are $10,$ and $40.$ We would like to map test scores to the range $[0\mathrm{.}0,1\mathrm{.}0].$ By min$-$max normalization, a value of $15$ for test score is transformed to$??$

Question $3(5\%)$

Using decimal scaling, salary bonus $=50$ scaled to$?$ Salary bonus $=21$ scaled to$?$

Question $4(35\%)$

A transaction database is a set of transactions. Each transaction is a set of items. For example, consider the following transaction database. It contains $6$ transactions $(t1,t2,$dots,$t5)$ and $5$ items $(1,2,3,4,5).$ For example, the first transaction represents the set of items $1,3$ and $4.$ It is important to note that an item is not allowed to appear twice in the same transaction and that items are assumed to be sorted by lexicographical order in a transaction.

$\backslash$table$[[$Transaction id$,$Items$],[$t$1,\{1,3,4\}$